The ideal counting function in cubic fields

Zhishan Yang

The ideal counting function in cubic fields

Number Theory 2015-03-05 v1

Authors: Zhishan Yang

Abstract

For a cubic algebraic extension $K$ of $\mathbb{Q}$ , the behavior of the ideal counting function is considered in this paper. Let $a_{K}(n)$ be the number of integral ideals of the field $K$ with norm $n$ . An asymptotic formula is given for the sum $\sum\limits_{n_{1}^2+n_{2}^2\leq x}a_{K}(n_{1}^2+n_{2}^2).$

Keywords

class number of quadratic fields divisor function

Cite

@article{arxiv.1503.01318,
  title  = {The ideal counting function in cubic fields},
  author = {Zhishan Yang},
  journal= {arXiv preprint arXiv:1503.01318},
  year   = {2015}
}

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